Need help with Magnetic Force (Calculus)

[ohshiznit422]

Ok, so. The formula is F=qv x B, meaning that the force vector is an orthogonal vector equal to the cross product of vectors qv and B. There are, however, 2 orthogonal vectors, in each direction. The thing I am having trouble understanding is why is one direction chosen over the other. I understand that this is demonstrated in the right hand rule, but the magnetic forces do not orient themselves in such a way just because that's the shape of my hand.

 

[dipole]

There is no reason $\vec{v}$ and $\vec{B}$ need to be orthogonal, but $\vec{F}$ is gaurenteed to be orthogonal to both. The right hand rule is just an easy way to remember the directions the vectors will point in in the special case when
$\vec{v}$ and $\vec{B}$ are orthogonal. If they aren't, then you have to actually do the work of computing the cross product.

 

[ohshiznit422]

I understand that the force vector will always be orthogonal, but there are 2 directions it can choose. For example, if qv is in the positive x direction, along the x axis, and b is in the positive y direction, along the y axis, the force vector can exist in either the positive OR negative z direction. I'm asking why the force aligns to any particular direction, and how it does so.

 

[Vorde]

It is just an arbitrary decision.

The bottom line is that we could use the left hand rule or the right hand rule in any calculation we want, as long as we use the same rule consistently.

 

[mfb]

The definition of the magnetic field direction is arbitrary - with a reversed definition, it would be a left-hand rule.
Swapping the sign of F or v would be possible mathematically, too, but I think this would be quite unintuitive.

 

[dipole]

Yea, it's because, arbitrarily, we choose to use a right-handed cooridnate system. If you used a left-handed system, things would have different signs.

If you want to ask the question of why the equation has that form at all, then you're asking something which probably has no answer - that's the way nature is.